## Fractals, baby! Vote now!

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- GCM
**Posts:**528**Joined:**Sat Jan 19, 2008 1:28 pm UTC**Location:**Metropolis City, Planet Kerwan, Solana Galaxy-
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### Fractals, baby! Vote now!

Please let me know if there's anything I've missed so I can totally ignore you! Because I can't do anything about it now.

I'm kinda new to this whole thing, so please don't berate me yet. I've gotten these off the web, and most of my though now goes to "they're very pretty". So do vote. Based on that. In fact, I'm not supposed to be even looking at this yet: Teach = "Dammit, Chris, you're not supposed to see this till college! Stop wasting your time on this and do your homework! I want that A, and I'm not going to get it if you don't freakin' study!"

I'm kinda new to this whole thing, so please don't berate me yet. I've gotten these off the web, and most of my though now goes to "they're very pretty". So do vote. Based on that. In fact, I'm not supposed to be even looking at this yet: Teach = "Dammit, Chris, you're not supposed to see this till college! Stop wasting your time on this and do your homework! I want that A, and I'm not going to get it if you don't freakin' study!"

Last edited by GCM on Thu May 08, 2008 12:05 pm UTC, edited 1 time in total.

All warfare is based on heavily-armed robotic commandos.

~Sun Tzu

Notes: My last avatar was "Vote Robot Nixon", so I'm gonna keep a list here.

~Sun Tzu

Notes: My last avatar was "Vote Robot Nixon", so I'm gonna keep a list here.

- 3.14159265...
- Irrational (?)
**Posts:**2413**Joined:**Thu Jan 18, 2007 12:05 am UTC**Location:**Ajax, Canada

### Re: Fractals, baby! Vote now!

I think you should provide pictures.

"The best times in life are the ones when you can genuinely add a "Bwa" to your "ha""- Chris Hastings

### Re: Fractals, baby! Vote now!

+13.14159265... wrote:I think you should provide pictures.

I don't feel like wikiing everything but the Mandelbrot set.

Code: Select all

`_=0,w=-1,(*t)(int,int);a()??<char*p="[gd\`

~/d~/\\b\x7F\177l*~/~djal{x}h!\005h";(++w

<033)?(putchar((*t)(w??(p:>,w?_:0XD)),a()

):0;%>O(x,l)??<_='['/7;{return!(x%(_-11))

?x??'l:x^(1+ ++l);}??>main(){t=&O;w=a();}

- 3.14159265...
- Irrational (?)
**Posts:**2413**Joined:**Thu Jan 18, 2007 12:05 am UTC**Location:**Ajax, Canada

### Re: Fractals, baby! Vote now!

Koch Snowflake

Sierpiński Triangle

Sierpiński Carpet

Cantor Set

Menger Sponge

Dragon Curve

Romanesco Broccoli

Mandelbrot Set

Peano Curve and Space filling Curve

Levy Flight

Kleinian Group

Julia Set

Lyapunov fractal

T-Square

Brownian Tree

Phoenix Set

Otter

Sierpiński Triangle

Sierpiński Carpet

Cantor Set

Menger Sponge

Dragon Curve

Romanesco Broccoli

Mandelbrot Set

Peano Curve and Space filling Curve

Levy Flight

Kleinian Group

Julia Set

Lyapunov fractal

T-Square

Brownian Tree

Phoenix Set

Otter

"The best times in life are the ones when you can genuinely add a "Bwa" to your "ha""- Chris Hastings

### Re: Fractals, baby! Vote now!

Aren't "space-filling curves" a category of fractals, not a specific one? And why isn't the Hilbert Curve on the list?

(The Sierpinski Gasket makes me want to cry.)

(The Sierpinski Gasket makes me want to cry.)

Felstaff wrote:Serves you goddamned right. I hope you're happy, Cake Ruiner

- skeptical scientist
- closed-minded spiritualist
**Posts:**6142**Joined:**Tue Nov 28, 2006 6:09 am UTC**Location:**San Francisco

### Re: Fractals, baby! Vote now!

I voted for space filling curves - they aren't as pretty as some of the others, but the fact that they exist is just too cool.

The Cantor set was a close second. Interesting fact: every perfect, compact, totally disconnected (nonempty) metric space is homeomorphic to the Cantor set. It also makes a fun exercise.

The Cantor set was a close second. Interesting fact: every perfect, compact, totally disconnected (nonempty) metric space is homeomorphic to the Cantor set. It also makes a fun exercise.

I'm looking forward to the day when the SNES emulator on my computer works by emulating the elementary particles in an actual, physical box with Nintendo stamped on the side.

"With math, all things are possible." —Rebecca Watson

"With math, all things are possible." —Rebecca Watson

### Re: Fractals, baby! Vote now!

I just looked up the Romanesco Broccoli. Imagine my surprise when I learned it's an actual broccoli- the edible flower of a sort of mustard plant. You know, the kind that grows in a field, and has leaves and roots and pollen. For gathering sunlight and water and whatnot. My mind is blown.

Felstaff wrote:Serves you goddamned right. I hope you're happy, Cake Ruiner

### Re: Fractals, baby! Vote now!

I voted for Mandelbrot, the dragon curve, and the Cantor set. Because you can't not vote for the Mandelbrot set, the dragon curve is just awesome, and the Cantor set is seriously weird.

You get 3 votes, so you can vote for both if you want.skeptical scientist wrote:I voted for space filling curves - they aren't as pretty as some of the others, but the fact that they exist is just too cool.

The Cantor set was a close second. Interesting fact: every perfect, compact, totally disconnected (nonempty) metric space is homeomorphic to the Cantor set. It also makes a fun exercise.

### Re: Fractals, baby! Vote now!

Mandelbrot and otter/duck: the Mandelbrot set contains approximate images of every Julia set in its family, and is itself a subset of a higher-dimensional fractal with various pretty cross-sections.

This is a placeholder until I think of something more creative to put here.

- Torn Apart By Dingos
**Posts:**817**Joined:**Thu Aug 03, 2006 2:27 am UTC

### Re: Fractals, baby! Vote now!

I love spacefilling curves! I'll use this thread to show an image I made. I mapped RGB (three-dimensional) to the unit square (2D dimensional) with a three- and a two-dimensional Sierpinski curve. I tried it with Hilbert and Peano curves as well, and I also tried using the HSV color space, but this one was the most pretty and symmetric.

- Dobblesworth
- Dobblesworth, here's the title you requested over three years ago. -Banana
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### Re: Fractals, baby! Vote now!

I put one vote down for Mandelbrot Set, as you can never deny the all-consuming awesomeness of a Rorscach Test on Fire. My others went to Sierpinski Triangle (or Triforce

^{9000}) and Koch Snowflake.- GCM
**Posts:**528**Joined:**Sat Jan 19, 2008 1:28 pm UTC**Location:**Metropolis City, Planet Kerwan, Solana Galaxy-
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### Re: Fractals, baby! Vote now!

Grates to π for the images; I really appreciate it. It's something I won't overlook next time.

Point taken, but I've not studied them before, so voila.

Silas wrote:Aren't "space-filling curves" a category of fractals, not a specific one? And why isn't the Hilbert Curve on the list?

Point taken, but I've not studied them before, so voila.

All warfare is based on heavily-armed robotic commandos.

~Sun Tzu

Notes: My last avatar was "Vote Robot Nixon", so I'm gonna keep a list here.

~Sun Tzu

Notes: My last avatar was "Vote Robot Nixon", so I'm gonna keep a list here.

### Re: Fractals, baby! Vote now!

The cool broccoli (which is a hybrid of broccoli and cauliflower), Mandelbrot and Phoenix are my favourite.

The Sierpinski Carpet makes me feel strangely empty inside O.o

The Sierpinski Carpet makes me feel strangely empty inside O.o

"I write what I see, the endless procession to the guillotine." ~ de Sade

### Re: Fractals, baby! Vote now!

I cast an Otter vote for an unavailable option: the classic fern fractal they always have you make in math/programming courses.

Rather large picture from Wikipedia in spoiler:

I just find it very aesthetically pleasing. Pretty, and sort of minimalist compared to the flashier ones like the Mandelbrot set. (Which also got a vote, along with the triangle)

I agree. Double for that Menger sponge. Although it does get a few points for looking reminiscent of a Borg cube.

Rather large picture from Wikipedia in spoiler:

**Spoiler:**

I just find it very aesthetically pleasing. Pretty, and sort of minimalist compared to the flashier ones like the Mandelbrot set. (Which also got a vote, along with the triangle)

Tiny wrote:The Sierpinski Carpet makes me feel strangely empty inside O.o

I agree. Double for that Menger sponge. Although it does get a few points for looking reminiscent of a Borg cube.

Beware the cows! Not all milk is enriched.

### Re: Fractals, baby! Vote now!

How about Quaternion Julia fractals? Hard to appreciate, as they have fractal dimensions between 3 and 4 but quite pretty anyway.

(please correct me if I have got my terminology wrong, I have had trouble finding good explanations on the subject)

(please correct me if I have got my terminology wrong, I have had trouble finding good explanations on the subject)

"Absolute precision buys the freedom to dream meaningfully." - Donal O' Shea: The Poincaré Conjecture.

"We need a reality check here. Roll a D20." - Algernon the Radish

"Should I marry W? Not unless she tells me what the other letters in her name are" Woody Allen.

"We need a reality check here. Roll a D20." - Algernon the Radish

"Should I marry W? Not unless she tells me what the other letters in her name are" Woody Allen.

### Re: Fractals, baby! Vote now!

They're still Julia sets, just plotted over a larger domain.

This is a placeholder until I think of something more creative to put here.

- Various Varieties
**Posts:**505**Joined:**Tue Mar 04, 2008 7:24 pm UTC

### Re: Fractals, baby! Vote now!

Robin S wrote:They're still Julia sets, just plotted over a larger domain.

Larger domain? In what sense? There are the same number of points in a 4 dimensional space as there are in a 2 dimensional space. (I'm sorry I can't help it )

In any case doesn't the fact that their domain is a non-abelian (non-commutative) group entitle them to their own category?

Does this Count

I wouldn't have thought so, Britain's coastline may be complicated, but it is not infinite. Even if you include the length of every last stream and drain that ends in the sea the it still has a dimensions of Length as opposed to Length^x.

PS. I question romanesco broccoli's claim to being a fractal too.

"Absolute precision buys the freedom to dream meaningfully." - Donal O' Shea: The Poincaré Conjecture.

"We need a reality check here. Roll a D20." - Algernon the Radish

"Should I marry W? Not unless she tells me what the other letters in her name are" Woody Allen.

"We need a reality check here. Roll a D20." - Algernon the Radish

"Should I marry W? Not unless she tells me what the other letters in her name are" Woody Allen.

### Re: Fractals, baby! Vote now!

I don't see why. Last time I checked, Julia sets were defined as sets of points for which behaviour under an iterated function was chaotic. Whether the domain happens to commute under multiplication is irrelevant.Frimble wrote:In any case doesn't the fact that their domain is a non-abelian (non-commutative) group entitle them to their own category?

As for the coastline / broccoli question, I would suggest that the inclusion of the latter in the poll would suggest that the former was legitimate. If you're questioning the validity of the inclusion of the latter, you could take it up with the original poster, but I would point out that none of the images are of the fractals themselves, but merely approximations to them - indeed, we are incapable of directly visualizing the fractals themselves, so that level of pedantry renders the poll useless.

This is a placeholder until I think of something more creative to put here.

### Re: Fractals, baby! Vote now!

The Oxford Concise Dictionary of Mathematics defines a Julia set as: 'The boundary of the set of points z

As this definition refers to the complex plane, it does not include quaternion Julia's.

It is my belief that a concept can be beautiful regardless of whether we can visualise it. After all who can visualise music? On second thoughts my debating skills are not up to arguing this... I had probably better stop now...

Alright the broccoli's an approximation to a fractal because it has a shape which if 'perfected' could potentially have an infinite surface area in a finite volume.

But by what argument does a coastline have an infinite length in a finite area?

_{0}in the complex plane for which the application of the function f(z)=z^{2}+c repeatedly to the point z_{0}produces a bounded sequence. The term may be used similarly for other functions as well.'As this definition refers to the complex plane, it does not include quaternion Julia's.

Robin S wrote:

As for the coastline / broccoli question, I would suggest that the inclusion of the latter in the poll would suggest that the former was legitimate. If you're questioning the validity of the inclusion of the latter, you could take it up with the original poster, but I would point out that none of the images are of the fractals themselves, but merely approximations to them - indeed, we are incapable of directly visualizing the fractals themselves, so that level of pedantry renders the poll useless.

It is my belief that a concept can be beautiful regardless of whether we can visualise it. After all who can visualise music? On second thoughts my debating skills are not up to arguing this... I had probably better stop now...

Alright the broccoli's an approximation to a fractal because it has a shape which if 'perfected' could potentially have an infinite surface area in a finite volume.

But by what argument does a coastline have an infinite length in a finite area?

"Absolute precision buys the freedom to dream meaningfully." - Donal O' Shea: The Poincaré Conjecture.

"We need a reality check here. Roll a D20." - Algernon the Radish

"Should I marry W? Not unless she tells me what the other letters in her name are" Woody Allen.

"We need a reality check here. Roll a D20." - Algernon the Radish

"Should I marry W? Not unless she tells me what the other letters in her name are" Woody Allen.

### Re: Fractals, baby! Vote now!

Phoenix Fractal FTW!

### Re: Fractals, baby! Vote now!

"Other functions" can have other domains. A quaternion Julia set is just a Julia set which happens to have been defined over the quaternions. Julia sets generated by the mapping z -> zFrimble wrote:The Oxford Concise Dictionary of Mathematics defines a Julia set as: 'The boundary of the set of points z_{0}in the complex plane for which the application of the function f(z)=z^{2}+c repeatedly to the point z_{0}produces a bounded sequence. The term may be used similarly for other functions as well.'

As this definition refers to the complex plane, it does not include quaternion Julia's.

^{2}+c are the best-known family in this category, and often the term "Julia set" applies to that family (and hence is restricted to the complex plane), but not necessarily.

I agree with you that things can be beautiful for reasons other than how they look. However, the main reason I (and, I think, many people) find fractals beautiful is because of how they look.It is my belief that a concept can be beautiful regardless of whether we can visualise it. After all who can visualise music? On second thoughts my debating skills are not up to arguing this... I had probably better stop now...

By the same argument.Alright the broccoli's an approximation to a fractal because it has a shape which if 'perfected' could potentially have an infinite surface area in a finite volume.

But by what argument does a coastline have an infinite length in a finite area?

This is a placeholder until I think of something more creative to put here.

- Luthen
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### Re: Fractals, baby! Vote now!

Dragon curve: duh ==>

I like it cause I can make it manually.

Mandelbrot is the poster child but I really only like the zoomed in sections (which shouldn't really make a difference should it?)

Never seen the Lyapunov before but it was just so insane it got my vote.

Would like to join the discussion but don't know enough of the maths behind them (did the Koch Snowflake for a friend's math assignment last year).

I like it cause I can make it manually.

Mandelbrot is the poster child but I really only like the zoomed in sections (which shouldn't really make a difference should it?)

Never seen the Lyapunov before but it was just so insane it got my vote.

Would like to join the discussion but don't know enough of the maths behind them (did the Koch Snowflake for a friend's math assignment last year).

My fancy new blog I am not a vampire! PM my location for a prize!*

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^{Terms + conditions changeable}### Re: Fractals, baby! Vote now!

Do I see the Burning Ship fractal?

I don't think I do.

This makes me sad, but the romanesco ______ is just slightly less cool, so it got my vote.

But damn, dude!

Burning ships.

I don't think I do.

This makes me sad, but the romanesco ______ is just slightly less cool, so it got my vote.

But damn, dude!

Burning ships.

### Re: Fractals, baby! Vote now!

How would one "perfect" a coastline? With the broccoli, there seems to be a pattern that one could follow. Not so much with the coast of England.Robin S wrote:By the same argument.Alright the broccoli's an approximation to a fractal because it has a shape which if 'perfected' could potentially have an infinite surface area in a finite volume.

But by what argument does a coastline have an infinite length in a finite area?

### Re: Fractals, baby! Vote now!

Using something like a fractal terrain generator.

This is a placeholder until I think of something more creative to put here.

- BeetlesBane
**Posts:**138**Joined:**Sun Apr 27, 2008 2:32 pm UTC**Location:**Not Chicago

### Re: Fractals, baby! Vote now!

From the definition of fractal at http://mathworld.wolfram.com/Fractal.html

"The prototypical example for a fractal is the length of a coastline measured with different length rulers."

"The prototypical example for a fractal is the length of a coastline measured with different length rulers."

### Re: Fractals, baby! Vote now!

Robin S wrote:"Other functions" can have other domains. A quaternion Julia set is just a Julia set which happens to have been defined over the quaternions. Julia sets generated by the mapping z -> zFrimble wrote:The Oxford Concise Dictionary of Mathematics defines a Julia set as: 'The boundary of the set of points z_{0}in the complex plane for which the application of the function f(z)=z^{2}+c repeatedly to the point z_{0}produces a bounded sequence. The term may be used similarly for other functions as well.'

As this definition refers to the complex plane, it does not include quaternion Julia's.^{2}+c are the best-known family in this category, and often the term "Julia set" applies to that family (and hence is restricted to the complex plane), but not necessarily.

Alright, The Julia set gets my vote then.

Robin S wrote:Using something like a fractal terrain generator.

A fractal terrain generator? Could you give an example? I have a program that can turn Julia/phoenix/mandlebrot fractals into 3d models, but I wouldn't call this a perfection of a coastline.

BeetlesBane wrote:From the definition of fractal at http://mathworld.wolfram.com/Fractal.html

"The prototypical example for a fractal is the length of a coastline measured with different length rulers."

The oxford dictionary defines a fractal in terms of its fractal dimension rather than in terms of symmetry. I'm not sure which is correct or even if the definitions are equivalent. The oxford definition seems less ambiguous in any case.

"We need a reality check here. Roll a D20." - Algernon the Radish

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- The Hyphenator
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### Re: Fractals, baby! Vote now!

Mandelbrot set. That is the prettiest and most amazing fractal ever. Nothing else comes close, in my opinion (except for the otter/duck set, of course).

The image link changes whenever I find a new cool website.

**Spoiler:**

- thornahawk
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### Re: Fractals, baby! Vote now!

I like Menger's sponge:

but the pentaflaked dodecahedron remains the fractal I love the most.

~ Werner

Code: Select all

`(* If[$VersionNumber < 5] *)`

Show[Graphics3D[

Join[{EdgeForm[], SurfaceColor[Hue[0.47], Hue[0.12], 1.38]},

Nest[Function[

g3d, (Flatten[

Cases[g3d, _Cuboid, Infinity]] /. {x_?NumericQ,

y_?NumericQ, z_?NumericQ} :> {x, y, z}/3 - #) & /@

Select[Flatten[Outer[List, Sequence @@ Table[2{-1, 0, 1}/3, {3}]],

2], (Count[#, 0] < 2) &]], {Cuboid[{-1, -1, -1}, {1, 1, 1}]},

4]], Boxed -> False]]

(* If[$VersionNumber >= 5] *)

Show[Graphics3D[

Join[{EdgeForm[], SurfaceColor[Hue[0.47], Hue[0.12], 1.38]},

Nest[Function[

g3d, (Flatten[

Cases[g3d, _Cuboid, Infinity]] /. {x_?NumericQ,

y_?NumericQ, z_?NumericQ} :> {x, y, z}/3 - #) & /@

Select[Tuples[{-2/3, 0, 2/3},

3], (Count[#, 0] < 2) &]], {Cuboid[{-1, -1, -1}, {1, 1, 1}]},

2]], Boxed -> False]]

but the pentaflaked dodecahedron remains the fractal I love the most.

~ Werner

John Dolan wrote:Cigarettes are insanely expensive and turn lots of poor people into cringing beggars.

E-mail!

### Re: Fractals, baby! Vote now!

I like this "clockwork arm" curve I came up with but haven't been able to find on the internet:

x = Sum[cos(t * 2^n) / 2^n | n ranges from 0 to infinity]

y = Sum[sin(t * 2^n) / 2^n | n ranges from 0 to infinity]

and t ranges from 0 to 2pi (of course)

Just imagine, on the first iteration, you have a pencil on the end of a rotating arm. The arm completes a rotation, drawing a circle

On the second iteration, you add another arm onto the end, one that is half as long and rotates twice as fast (in relation to the stationary drawing paper, not the first arm: I tried that and, to me, it doesn't look as cool.)

The third iteration adds a third arm one eighth the length of the original and rotating eight times as fast.

I might download a crappy free graphing program and generate a picture to show you.

It looks a little like an alien's head.

EDIT: Actually, that was really quick and easy. Here's eight iterations (surely overkill):

And a zoom in:

x = Sum[cos(t * 2^n) / 2^n | n ranges from 0 to infinity]

y = Sum[sin(t * 2^n) / 2^n | n ranges from 0 to infinity]

and t ranges from 0 to 2pi (of course)

Just imagine, on the first iteration, you have a pencil on the end of a rotating arm. The arm completes a rotation, drawing a circle

On the second iteration, you add another arm onto the end, one that is half as long and rotates twice as fast (in relation to the stationary drawing paper, not the first arm: I tried that and, to me, it doesn't look as cool.)

The third iteration adds a third arm one eighth the length of the original and rotating eight times as fast.

I might download a crappy free graphing program and generate a picture to show you.

It looks a little like an alien's head.

EDIT: Actually, that was really quick and easy. Here's eight iterations (surely overkill):

**Spoiler:**

And a zoom in:

**Spoiler:**

Totally random totally awesome SF quote:

Jorane Sutt put the tips of carefully-manicured fingers together and said, "It's something of a puzzle. In fact--and this is in the strictest confidence--it may be another one of Hari Seldon's crises."

Jorane Sutt put the tips of carefully-manicured fingers together and said, "It's something of a puzzle. In fact--and this is in the strictest confidence--it may be another one of Hari Seldon's crises."

- thornahawk
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### Re: Fractals, baby! Vote now!

atimholt wrote:I like this "clockwork arm" curve I came up with but haven't been able to find on the internet:

x = Sum[cos(t * 2^n) / 2^n | n ranges from 0 to infinity]

y = Sum[sin(t * 2^n) / 2^n | n ranges from 0 to infinity]

and t ranges from 0 to 2pi (of course)

**Spoiler:**

If it helps anything, the functions you used bear a resemblance to the Fourier series studied by Weierstrass and Riemann.

~ Werner

John Dolan wrote:Cigarettes are insanely expensive and turn lots of poor people into cringing beggars.

E-mail!

### Re: Fractals, baby! Vote now!

I voted for space filling, because they are useful. Mandelbrot for prettiness.

- DrProfessorPhD
**Posts:**55**Joined:**Sat Oct 11, 2008 5:35 pm UTC

### Re: Fractals, baby! Vote now!

Mandelbrot, Phoenix, and Otter (Burning ship)

I am probably a swordfighting octopus. In case you can't tell.

### Re: Fractals, baby! Vote now!

Hi Frimble,

I have an image of a "tornado-lobster" quaternion Julia set. I thought you might be interested.

It is Figure 14, on page 17 of this paper: http://cavekitty.ca/inv_ssa.pdf

I have an image of a "tornado-lobster" quaternion Julia set. I thought you might be interested.

It is Figure 14, on page 17 of this paper: http://cavekitty.ca/inv_ssa.pdf

### Re: Fractals, baby! Vote now!

How could you leave out http://en.wikipedia.org/wiki/Burning_Ship_fractal?

(I voted mandelbrot since they are closely related)

(I voted mandelbrot since they are closely related)

- parallax
**Posts:**157**Joined:**Wed Jan 31, 2007 5:06 pm UTC**Location:**The Emergency Intelligence Incinerator

### Re: Fractals, baby! Vote now!

The coastline of Britain is a fractal. It has a fractal dimension of 1.25. Granted, it may not be an exact fractal as the coastline itself is poorly defined at smaller scales, but it is statistically self-similar at all larger scales.

Cake and grief counseling will be available at the conclusion of the test.

### Re: Fractals, baby! Vote now!

I voted Mandelbrot set and Dragon curve.

Mandelbrot set 'cause I know it inside out because of a project I had to do on it (set of bounded numbers on the complex plane... forgotten the formula) and the Dragon curve because iterations of it appear on the chapter pages of Jurassic Park, which is just so awesome.

Mandelbrot set 'cause I know it inside out because of a project I had to do on it (set of bounded numbers on the complex plane... forgotten the formula) and the Dragon curve because iterations of it appear on the chapter pages of Jurassic Park, which is just so awesome.

"It's kinda fun to do the impossible" - Walt Disney

### Re: Fractals, baby! Vote now!

Pathological monsters! Every one of them is a splinter in my eye!

The lyapunov is all... curvaceous. Even better, I think I understand the math behind all the pretty curves.

[edit] The coastline of Britain is infinitely long.

The lyapunov is all... curvaceous. Even better, I think I understand the math behind all the pretty curves.

[edit] The coastline of Britain is infinitely long.

### Re: Fractals, baby! Vote now!

if anyone can find me a fractal with a Hausdroff dimension of π, that would be my favourite.

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